src/HOL/Tools/datatype_abs_proofs.ML
author paulson
Tue May 22 17:56:06 2007 +0200 (2007-05-22)
changeset 23075 69e30a7e8880
parent 22994 02440636214f
child 23590 ad95084a5c63
permissions -rw-r--r--
Some hacks for SPASS format
     1 (*  Title:      HOL/Tools/datatype_abs_proofs.ML
     2     ID:         $Id$
     3     Author:     Stefan Berghofer, TU Muenchen
     4 
     5 Proofs and defintions independent of concrete representation
     6 of datatypes  (i.e. requiring only abstract properties such as
     7 injectivity / distinctness of constructors and induction)
     8 
     9  - case distinction (exhaustion) theorems
    10  - characteristic equations for primrec combinators
    11  - characteristic equations for case combinators
    12  - equations for splitting "P (case ...)" expressions
    13  - datatype size function
    14  - "nchotomy" and "case_cong" theorems for TFL
    15 
    16 *)
    17 
    18 signature DATATYPE_ABS_PROOFS =
    19 sig
    20   val prove_casedist_thms : string list ->
    21     DatatypeAux.descr list -> (string * sort) list -> thm ->
    22     attribute list -> theory -> thm list * theory
    23   val prove_primrec_thms : bool -> string list ->
    24     DatatypeAux.descr list -> (string * sort) list ->
    25       DatatypeAux.datatype_info Symtab.table -> thm list list -> thm list list ->
    26         simpset -> thm -> theory -> (string list * thm list) * theory
    27   val prove_case_thms : bool -> string list ->
    28     DatatypeAux.descr list -> (string * sort) list ->
    29       string list -> thm list -> theory -> (thm list list * string list) * theory
    30   val prove_split_thms : string list ->
    31     DatatypeAux.descr list -> (string * sort) list ->
    32       thm list list -> thm list list -> thm list -> thm list list -> theory ->
    33         (thm * thm) list * theory
    34   val prove_size_thms : bool -> string list ->
    35     DatatypeAux.descr list -> (string * sort) list ->
    36       string list -> thm list -> theory -> thm list * theory
    37   val prove_nchotomys : string list -> DatatypeAux.descr list ->
    38     (string * sort) list -> thm list -> theory -> thm list * theory
    39   val prove_weak_case_congs : string list -> DatatypeAux.descr list ->
    40     (string * sort) list -> theory -> thm list * theory
    41   val prove_case_congs : string list ->
    42     DatatypeAux.descr list -> (string * sort) list ->
    43       thm list -> thm list list -> theory -> thm list * theory
    44 end;
    45 
    46 structure DatatypeAbsProofs: DATATYPE_ABS_PROOFS =
    47 struct
    48 
    49 open DatatypeAux;
    50 
    51 (************************ case distinction theorems ***************************)
    52 
    53 fun prove_casedist_thms new_type_names descr sorts induct case_names_exhausts thy =
    54   let
    55     val _ = message "Proving case distinction theorems ...";
    56 
    57     val descr' = List.concat descr;
    58     val recTs = get_rec_types descr' sorts;
    59     val newTs = Library.take (length (hd descr), recTs);
    60 
    61     val {maxidx, ...} = rep_thm induct;
    62     val induct_Ps = map head_of (HOLogic.dest_conj (HOLogic.dest_Trueprop (concl_of induct)));
    63 
    64     fun prove_casedist_thm ((i, t), T) =
    65       let
    66         val dummyPs = map (fn (Var (_, Type (_, [T', T'']))) =>
    67           Abs ("z", T', Const ("True", T''))) induct_Ps;
    68         val P = Abs ("z", T, HOLogic.imp $ HOLogic.mk_eq (Var (("a", maxidx+1), T), Bound 0) $
    69           Var (("P", 0), HOLogic.boolT))
    70         val insts = Library.take (i, dummyPs) @ (P::(Library.drop (i + 1, dummyPs)));
    71         val cert = cterm_of thy;
    72         val insts' = (map cert induct_Ps) ~~ (map cert insts);
    73         val induct' = refl RS ((List.nth
    74           (split_conj_thm (cterm_instantiate insts' induct), i)) RSN (2, rev_mp))
    75 
    76       in
    77         Goal.prove_global thy [] (Logic.strip_imp_prems t) (Logic.strip_imp_concl t)
    78           (fn prems => EVERY
    79             [rtac induct' 1,
    80              REPEAT (rtac TrueI 1),
    81              REPEAT ((rtac impI 1) THEN (eresolve_tac prems 1)),
    82              REPEAT (rtac TrueI 1)])
    83       end;
    84 
    85     val casedist_thms = map prove_casedist_thm ((0 upto (length newTs - 1)) ~~
    86       (DatatypeProp.make_casedists descr sorts) ~~ newTs)
    87   in
    88     thy
    89     |> store_thms_atts "exhaust" new_type_names (map single case_names_exhausts) casedist_thms
    90   end;
    91 
    92 
    93 (*************************** primrec combinators ******************************)
    94 
    95 fun prove_primrec_thms flat_names new_type_names descr sorts
    96     (dt_info : datatype_info Symtab.table) constr_inject dist_rewrites dist_ss induct thy =
    97   let
    98     val _ = message "Constructing primrec combinators ...";
    99 
   100     val big_name = space_implode "_" new_type_names;
   101     val thy0 = add_path flat_names big_name thy;
   102 
   103     val descr' = List.concat descr;
   104     val recTs = get_rec_types descr' sorts;
   105     val used = foldr add_typ_tfree_names [] recTs;
   106     val newTs = Library.take (length (hd descr), recTs);
   107 
   108     val induct_Ps = map head_of (HOLogic.dest_conj (HOLogic.dest_Trueprop (concl_of induct)));
   109 
   110     val big_rec_name' = big_name ^ "_rec_set";
   111     val rec_set_names' =
   112       if length descr' = 1 then [big_rec_name'] else
   113         map ((curry (op ^) (big_rec_name' ^ "_")) o string_of_int)
   114           (1 upto (length descr'));
   115     val rec_set_names = map (Sign.full_name thy0) rec_set_names';
   116 
   117     val (rec_result_Ts, reccomb_fn_Ts) = DatatypeProp.make_primrec_Ts descr sorts used;
   118 
   119     val rec_set_Ts = map (fn (T1, T2) =>
   120       reccomb_fn_Ts @ [T1, T2] ---> HOLogic.boolT) (recTs ~~ rec_result_Ts);
   121 
   122     val rec_fns = map (uncurry (mk_Free "f"))
   123       (reccomb_fn_Ts ~~ (1 upto (length reccomb_fn_Ts)));
   124     val rec_sets' = map (fn c => list_comb (Free c, rec_fns))
   125       (rec_set_names' ~~ rec_set_Ts);
   126     val rec_sets = map (fn c => list_comb (Const c, rec_fns))
   127       (rec_set_names ~~ rec_set_Ts);
   128 
   129     (* introduction rules for graph of primrec function *)
   130 
   131     fun make_rec_intr T rec_set ((rec_intr_ts, l), (cname, cargs)) =
   132       let
   133         fun mk_prem ((dt, U), (j, k, prems, t1s, t2s)) =
   134           let val free1 = mk_Free "x" U j
   135           in (case (strip_dtyp dt, strip_type U) of
   136              ((_, DtRec m), (Us, _)) =>
   137                let
   138                  val free2 = mk_Free "y" (Us ---> List.nth (rec_result_Ts, m)) k;
   139                  val i = length Us
   140                in (j + 1, k + 1, HOLogic.mk_Trueprop (HOLogic.list_all
   141                      (map (pair "x") Us, List.nth (rec_sets', m) $
   142                        app_bnds free1 i $ app_bnds free2 i)) :: prems,
   143                    free1::t1s, free2::t2s)
   144                end
   145            | _ => (j + 1, k, prems, free1::t1s, t2s))
   146           end;
   147 
   148         val Ts = map (typ_of_dtyp descr' sorts) cargs;
   149         val (_, _, prems, t1s, t2s) = foldr mk_prem (1, 1, [], [], []) (cargs ~~ Ts)
   150 
   151       in (rec_intr_ts @ [Logic.list_implies (prems, HOLogic.mk_Trueprop
   152         (rec_set $ list_comb (Const (cname, Ts ---> T), t1s) $
   153           list_comb (List.nth (rec_fns, l), t1s @ t2s)))], l + 1)
   154       end;
   155 
   156     val (rec_intr_ts, _) = Library.foldl (fn (x, ((d, T), set_name)) =>
   157       Library.foldl (make_rec_intr T set_name) (x, #3 (snd d)))
   158         (([], 0), descr' ~~ recTs ~~ rec_sets');
   159 
   160     val ({intrs = rec_intrs, elims = rec_elims, ...}, thy1) =
   161       setmp InductivePackage.quiet_mode (!quiet_mode)
   162         (InductivePackage.add_inductive_global false big_rec_name' false false true
   163            (map (fn (s, T) => (s, SOME T, NoSyn)) (rec_set_names' ~~ rec_set_Ts))
   164            (map (apsnd SOME o dest_Free) rec_fns)
   165            (map (fn x => (("", []), x)) rec_intr_ts) []) thy0;
   166 
   167     (* prove uniqueness and termination of primrec combinators *)
   168 
   169     val _ = message "Proving termination and uniqueness of primrec functions ...";
   170 
   171     fun mk_unique_tac ((tac, intrs), ((((i, (tname, _, constrs)), elim), T), T')) =
   172       let
   173         val distinct_tac =
   174           (if i < length newTs then
   175              full_simp_tac (HOL_ss addsimps (List.nth (dist_rewrites, i))) 1
   176            else full_simp_tac dist_ss 1);
   177 
   178         val inject = map (fn r => r RS iffD1)
   179           (if i < length newTs then List.nth (constr_inject, i)
   180             else #inject (the (Symtab.lookup dt_info tname)));
   181 
   182         fun mk_unique_constr_tac n ((tac, intr::intrs, j), (cname, cargs)) =
   183           let
   184             val k = length (List.filter is_rec_type cargs)
   185 
   186           in (EVERY [DETERM tac,
   187                 REPEAT (etac ex1E 1), rtac ex1I 1,
   188                 DEPTH_SOLVE_1 (ares_tac [intr] 1),
   189                 REPEAT_DETERM_N k (etac thin_rl 1 THEN rotate_tac 1 1),
   190                 etac elim 1,
   191                 REPEAT_DETERM_N j distinct_tac,
   192                 TRY (dresolve_tac inject 1),
   193                 REPEAT (etac conjE 1), hyp_subst_tac 1,
   194                 REPEAT (EVERY [etac allE 1, dtac mp 1, atac 1]),
   195                 TRY (hyp_subst_tac 1),
   196                 rtac refl 1,
   197                 REPEAT_DETERM_N (n - j - 1) distinct_tac],
   198               intrs, j + 1)
   199           end;
   200 
   201         val (tac', intrs', _) = Library.foldl (mk_unique_constr_tac (length constrs))
   202           ((tac, intrs, 0), constrs);
   203 
   204       in (tac', intrs') end;
   205 
   206     val rec_unique_thms =
   207       let
   208         val rec_unique_ts = map (fn (((set_t, T1), T2), i) =>
   209           Const ("Ex1", (T2 --> HOLogic.boolT) --> HOLogic.boolT) $
   210             absfree ("y", T2, set_t $ mk_Free "x" T1 i $ Free ("y", T2)))
   211               (rec_sets ~~ recTs ~~ rec_result_Ts ~~ (1 upto length recTs));
   212         val cert = cterm_of thy1
   213         val insts = map (fn ((i, T), t) => absfree ("x" ^ (string_of_int i), T, t))
   214           ((1 upto length recTs) ~~ recTs ~~ rec_unique_ts);
   215         val induct' = cterm_instantiate ((map cert induct_Ps) ~~
   216           (map cert insts)) induct;
   217         val (tac, _) = Library.foldl mk_unique_tac
   218           (((rtac induct' THEN_ALL_NEW ObjectLogic.atomize_tac) 1
   219               THEN rewtac (mk_meta_eq choice_eq), rec_intrs),
   220             descr' ~~ rec_elims ~~ recTs ~~ rec_result_Ts);
   221 
   222       in split_conj_thm (Goal.prove_global thy1 [] []
   223         (HOLogic.mk_Trueprop (mk_conj rec_unique_ts)) (K tac))
   224       end;
   225 
   226     val rec_total_thms = map (fn r => r RS theI') rec_unique_thms;
   227 
   228     (* define primrec combinators *)
   229 
   230     val big_reccomb_name = (space_implode "_" new_type_names) ^ "_rec";
   231     val reccomb_names = map (Sign.full_name thy1)
   232       (if length descr' = 1 then [big_reccomb_name] else
   233         (map ((curry (op ^) (big_reccomb_name ^ "_")) o string_of_int)
   234           (1 upto (length descr'))));
   235     val reccombs = map (fn ((name, T), T') => list_comb
   236       (Const (name, reccomb_fn_Ts @ [T] ---> T'), rec_fns))
   237         (reccomb_names ~~ recTs ~~ rec_result_Ts);
   238 
   239     val (reccomb_defs, thy2) =
   240       thy1
   241       |> Theory.add_consts_i (map (fn ((name, T), T') =>
   242           (Sign.base_name name, reccomb_fn_Ts @ [T] ---> T', NoSyn))
   243           (reccomb_names ~~ recTs ~~ rec_result_Ts))
   244       |> (PureThy.add_defs_i false o map Thm.no_attributes) (map (fn ((((name, comb), set), T), T') =>
   245           ((Sign.base_name name) ^ "_def", Logic.mk_equals (comb, absfree ("x", T,
   246            Const ("The", (T' --> HOLogic.boolT) --> T') $ absfree ("y", T',
   247              set $ Free ("x", T) $ Free ("y", T'))))))
   248                (reccomb_names ~~ reccombs ~~ rec_sets ~~ recTs ~~ rec_result_Ts))
   249       ||> parent_path flat_names;
   250 
   251 
   252     (* prove characteristic equations for primrec combinators *)
   253 
   254     val _ = message "Proving characteristic theorems for primrec combinators ..."
   255 
   256     val rec_thms = map (fn t => Goal.prove_global thy2 [] [] t
   257       (fn _ => EVERY
   258         [rewrite_goals_tac reccomb_defs,
   259          rtac the1_equality 1,
   260          resolve_tac rec_unique_thms 1,
   261          resolve_tac rec_intrs 1,
   262          REPEAT (rtac allI 1 ORELSE resolve_tac rec_total_thms 1)]))
   263            (DatatypeProp.make_primrecs new_type_names descr sorts thy2)
   264 
   265   in
   266     thy2
   267     |> Theory.add_path (space_implode "_" new_type_names)
   268     |> PureThy.add_thmss [(("recs", rec_thms), [])]
   269     ||> Theory.parent_path
   270     |-> (fn thms => pair (reccomb_names, Library.flat thms))
   271   end;
   272 
   273 
   274 (***************************** case combinators *******************************)
   275 
   276 fun prove_case_thms flat_names new_type_names descr sorts reccomb_names primrec_thms thy =
   277   let
   278     val _ = message "Proving characteristic theorems for case combinators ...";
   279 
   280     val thy1 = add_path flat_names (space_implode "_" new_type_names) thy;
   281 
   282     val descr' = List.concat descr;
   283     val recTs = get_rec_types descr' sorts;
   284     val used = foldr add_typ_tfree_names [] recTs;
   285     val newTs = Library.take (length (hd descr), recTs);
   286     val T' = TFree (Name.variant used "'t", HOLogic.typeS);
   287 
   288     fun mk_dummyT dt = binder_types (typ_of_dtyp descr' sorts dt) ---> T';
   289 
   290     val case_dummy_fns = map (fn (_, (_, _, constrs)) => map (fn (_, cargs) =>
   291       let
   292         val Ts = map (typ_of_dtyp descr' sorts) cargs;
   293         val Ts' = map mk_dummyT (List.filter is_rec_type cargs)
   294       in Const ("arbitrary", Ts @ Ts' ---> T')
   295       end) constrs) descr';
   296 
   297     val case_names = map (fn s => Sign.full_name thy1 (s ^ "_case")) new_type_names;
   298 
   299     (* define case combinators via primrec combinators *)
   300 
   301     val (case_defs, thy2) = Library.foldl (fn ((defs, thy),
   302       ((((i, (_, _, constrs)), T), name), recname)) =>
   303         let
   304           val (fns1, fns2) = ListPair.unzip (map (fn ((_, cargs), j) =>
   305             let
   306               val Ts = map (typ_of_dtyp descr' sorts) cargs;
   307               val Ts' = Ts @ map mk_dummyT (List.filter is_rec_type cargs);
   308               val frees' = map (uncurry (mk_Free "x")) (Ts' ~~ (1 upto length Ts'));
   309               val frees = Library.take (length cargs, frees');
   310               val free = mk_Free "f" (Ts ---> T') j
   311             in
   312              (free, list_abs_free (map dest_Free frees',
   313                list_comb (free, frees)))
   314             end) (constrs ~~ (1 upto length constrs)));
   315 
   316           val caseT = (map (snd o dest_Free) fns1) @ [T] ---> T';
   317           val fns = (List.concat (Library.take (i, case_dummy_fns))) @
   318             fns2 @ (List.concat (Library.drop (i + 1, case_dummy_fns)));
   319           val reccomb = Const (recname, (map fastype_of fns) @ [T] ---> T');
   320           val decl = (Sign.base_name name, caseT, NoSyn);
   321           val def = ((Sign.base_name name) ^ "_def",
   322             Logic.mk_equals (list_comb (Const (name, caseT), fns1),
   323               list_comb (reccomb, (List.concat (Library.take (i, case_dummy_fns))) @
   324                 fns2 @ (List.concat (Library.drop (i + 1, case_dummy_fns))) )));
   325           val ([def_thm], thy') =
   326             thy
   327             |> Sign.add_consts_authentic [decl]
   328             |> (PureThy.add_defs_i false o map Thm.no_attributes) [def];
   329 
   330         in (defs @ [def_thm], thy')
   331         end) (([], thy1), (hd descr) ~~ newTs ~~ case_names ~~
   332           (Library.take (length newTs, reccomb_names)));
   333 
   334     val case_thms = map (map (fn t => Goal.prove_global thy2 [] [] t
   335       (fn _ => EVERY [rewrite_goals_tac (case_defs @ map mk_meta_eq primrec_thms), rtac refl 1])))
   336           (DatatypeProp.make_cases new_type_names descr sorts thy2)
   337 
   338   in
   339     thy2
   340     |> parent_path flat_names
   341     |> store_thmss "cases" new_type_names case_thms
   342     |-> (fn thmss => pair (thmss, case_names))
   343   end;
   344 
   345 
   346 (******************************* case splitting *******************************)
   347 
   348 fun prove_split_thms new_type_names descr sorts constr_inject dist_rewrites
   349     casedist_thms case_thms thy =
   350   let
   351     val _ = message "Proving equations for case splitting ...";
   352 
   353     val descr' = List.concat descr;
   354     val recTs = get_rec_types descr' sorts;
   355     val newTs = Library.take (length (hd descr), recTs);
   356 
   357     fun prove_split_thms ((((((t1, t2), inject), dist_rewrites'),
   358         exhaustion), case_thms'), T) =
   359       let
   360         val cert = cterm_of thy;
   361         val _ $ (_ $ lhs $ _) = hd (Logic.strip_assums_hyp (hd (prems_of exhaustion)));
   362         val exhaustion' = cterm_instantiate
   363           [(cert lhs, cert (Free ("x", T)))] exhaustion;
   364         val tacf = K (EVERY [rtac exhaustion' 1, ALLGOALS (asm_simp_tac
   365           (HOL_ss addsimps (dist_rewrites' @ inject @ case_thms')))])
   366       in
   367         (Goal.prove_global thy [] [] t1 tacf,
   368          Goal.prove_global thy [] [] t2 tacf)
   369       end;
   370 
   371     val split_thm_pairs = map prove_split_thms
   372       ((DatatypeProp.make_splits new_type_names descr sorts thy) ~~ constr_inject ~~
   373         dist_rewrites ~~ casedist_thms ~~ case_thms ~~ newTs);
   374 
   375     val (split_thms, split_asm_thms) = ListPair.unzip split_thm_pairs
   376 
   377   in
   378     thy
   379     |> store_thms "split" new_type_names split_thms
   380     ||>> store_thms "split_asm" new_type_names split_asm_thms
   381     |-> (fn (thms1, thms2) => pair (thms1 ~~ thms2))
   382   end;
   383 
   384 (******************************* size functions *******************************)
   385 
   386 fun prove_size_thms flat_names new_type_names descr sorts reccomb_names primrec_thms thy =
   387   if exists (fn (_, (_, _, constrs)) => exists (fn (_, cargs) => exists (fn dt =>
   388     is_rec_type dt andalso not (null (fst (strip_dtyp dt)))) cargs) constrs)
   389       (List.concat descr)
   390   then
   391     ([], thy)
   392   else
   393   let
   394     val _ = message "Proving equations for size function ...";
   395 
   396     val big_name = space_implode "_" new_type_names;
   397     val thy1 = add_path flat_names big_name thy;
   398 
   399     val descr' = flat descr;
   400     val recTs = get_rec_types descr' sorts;
   401 
   402     val Const (size_name, _) = HOLogic.size_const dummyT;
   403     val size_names = replicate (length (hd descr)) size_name @
   404       map (Sign.full_name thy1) (DatatypeProp.indexify_names
   405         (map (fn T => name_of_typ T ^ "_size") (Library.drop (length (hd descr), recTs))));
   406     val def_names = map (fn s => s ^ "_def") (DatatypeProp.indexify_names
   407       (map (fn T => name_of_typ T ^ "_size") recTs));
   408 
   409     fun plus (t1, t2) =
   410       Const ("HOL.plus_class.plus", HOLogic.natT --> HOLogic.natT --> HOLogic.natT) $ t1 $ t2;
   411 
   412     fun make_sizefun (_, cargs) =
   413       let
   414         val Ts = map (typ_of_dtyp descr' sorts) cargs;
   415         val k = length (filter is_rec_type cargs);
   416         val t = if k = 0 then HOLogic.zero else
   417           foldl1 plus (map Bound (k - 1 downto 0) @ [HOLogic.Suc_zero])
   418       in
   419         foldr (fn (T, t') => Abs ("x", T, t')) t (Ts @ replicate k HOLogic.natT)
   420       end;
   421 
   422     val fs = maps (fn (_, (_, _, constrs)) => map make_sizefun constrs) descr';
   423     val fTs = map fastype_of fs;
   424 
   425     fun instance_size_class tyco thy =
   426       let
   427         val n = Sign.arity_number thy tyco;
   428       in
   429         thy
   430         |> AxClass.prove_arity (tyco, replicate n HOLogic.typeS, [HOLogic.class_size])
   431              (ClassPackage.intro_classes_tac [])
   432       end
   433 
   434     val (size_def_thms, thy') =
   435       thy1
   436       |> Theory.add_consts_i (map (fn (s, T) =>
   437            (Sign.base_name s, T --> HOLogic.natT, NoSyn))
   438            (Library.drop (length (hd descr), size_names ~~ recTs)))
   439       |> fold (fn (_, (name, _, _)) => instance_size_class name) descr'
   440       |> PureThy.add_defs_i true (map (Thm.no_attributes o (fn (((s, T), def_name), rec_name) =>
   441            (def_name, Logic.mk_equals (Const (s, T --> HOLogic.natT),
   442             list_comb (Const (rec_name, fTs @ [T] ---> HOLogic.natT), fs)))))
   443             (size_names ~~ recTs ~~ def_names ~~ reccomb_names))
   444       ||> parent_path flat_names;
   445 
   446     val rewrites = size_def_thms @ map mk_meta_eq primrec_thms;
   447 
   448     val size_thms = map (fn t => Goal.prove_global thy' [] [] t
   449       (fn _ => EVERY [rewrite_goals_tac rewrites, rtac refl 1]))
   450         (DatatypeProp.make_size descr sorts thy')
   451 
   452   in
   453     thy'
   454     |> Theory.add_path big_name
   455     |> PureThy.add_thmss [(("size", size_thms), [])]
   456     ||> Theory.parent_path
   457     |-> (fn thmss => pair (flat thmss))
   458   end;
   459 
   460 fun prove_weak_case_congs new_type_names descr sorts thy =
   461   let
   462     fun prove_weak_case_cong t =
   463        Goal.prove_global thy [] (Logic.strip_imp_prems t) (Logic.strip_imp_concl t)
   464          (fn prems => EVERY [rtac ((hd prems) RS arg_cong) 1])
   465 
   466     val weak_case_congs = map prove_weak_case_cong (DatatypeProp.make_weak_case_congs
   467       new_type_names descr sorts thy)
   468 
   469   in thy |> store_thms "weak_case_cong" new_type_names weak_case_congs end;
   470 
   471 (************************* additional theorems for TFL ************************)
   472 
   473 fun prove_nchotomys new_type_names descr sorts casedist_thms thy =
   474   let
   475     val _ = message "Proving additional theorems for TFL ...";
   476 
   477     fun prove_nchotomy (t, exhaustion) =
   478       let
   479         (* For goal i, select the correct disjunct to attack, then prove it *)
   480         fun tac i 0 = EVERY [TRY (rtac disjI1 i),
   481               hyp_subst_tac i, REPEAT (rtac exI i), rtac refl i]
   482           | tac i n = rtac disjI2 i THEN tac i (n - 1)
   483       in 
   484         Goal.prove_global thy [] [] t (fn _ =>
   485           EVERY [rtac allI 1,
   486            exh_tac (K exhaustion) 1,
   487            ALLGOALS (fn i => tac i (i-1))])
   488       end;
   489 
   490     val nchotomys =
   491       map prove_nchotomy (DatatypeProp.make_nchotomys descr sorts ~~ casedist_thms)
   492 
   493   in thy |> store_thms "nchotomy" new_type_names nchotomys end;
   494 
   495 fun prove_case_congs new_type_names descr sorts nchotomys case_thms thy =
   496   let
   497     fun prove_case_cong ((t, nchotomy), case_rewrites) =
   498       let
   499         val (Const ("==>", _) $ tm $ _) = t;
   500         val (Const ("Trueprop", _) $ (Const ("op =", _) $ _ $ Ma)) = tm;
   501         val cert = cterm_of thy;
   502         val nchotomy' = nchotomy RS spec;
   503         val nchotomy'' = cterm_instantiate
   504           [(cert (hd (add_term_vars (concl_of nchotomy', []))), cert Ma)] nchotomy'
   505       in
   506         Goal.prove_global thy [] (Logic.strip_imp_prems t) (Logic.strip_imp_concl t)
   507           (fn prems => 
   508             let val simplify = asm_simp_tac (HOL_ss addsimps (prems @ case_rewrites))
   509             in EVERY [simp_tac (HOL_ss addsimps [hd prems]) 1,
   510                 cut_facts_tac [nchotomy''] 1,
   511                 REPEAT (etac disjE 1 THEN REPEAT (etac exE 1) THEN simplify 1),
   512                 REPEAT (etac exE 1) THEN simplify 1 (* Get last disjunct *)]
   513             end)
   514       end;
   515 
   516     val case_congs = map prove_case_cong (DatatypeProp.make_case_congs
   517       new_type_names descr sorts thy ~~ nchotomys ~~ case_thms)
   518 
   519   in thy |> store_thms "case_cong" new_type_names case_congs end;
   520 
   521 end;